Array

An array is a ``list of lists'' with the length of each level of list the same. The size (sometimes called the ``shape'')of a -dimensional array is then indicated as . The most commontype of array encountered is the 2-D rectangular array having columns and rows. If , a square arrayresults. Sometimes, the order of the elements in an array is significant (as in a Matrix), whereas at other times,arrays which are equivalent modulo reflections (and rotations, in the case of a square array) are considered identical (asin a Magic Square or Prime Array).

In order to exhaustively list the number of distinct arrays of a given shape with each element being one of possiblechoices, the naive algorithm of running through each case and checking to see whether it's equivalent to an earlier oneis already just about as efficient as can be. The running time must be at least the number of answers, and this is soclose to that the difference isn't significant.

However, finding the number of possible arrays of a given shape is much easier, and an exact formula can be obtained usingthe Polya Enumeration Theorem. For the simple case of an array, even this proves unnecessary since thereare only a few possible symmetry types, allowing the possibilities to be counted explicitly. For example, consider the caseof and Even and distinct, so only reflections need be included. To take a specific case, let and so the array looks like

In general, it is therefore true that

• Pseudorhombicuboctahedron
• Pseudoscalar
• Pseudosmarandache Function
• Pseudosphere
• Pseudosquare
• Pseudotensor
• Pseudovector
• Psi Function
• p-Signature
• PSLQ Algorithm
• PSOS Algorithm
• P-Symbol
• Ptolemy Inequality
• Ptolemy's Theorem
• Public-Key Cryptography
• Puiseaux's Theorem
• Pullback Map
• Pulse Function
• Purser's Theorem
• Pursuit Curve
• Push
• Puzzle
• P-Value
• Pyramid
• Pyramidal Frustum